This thesis is concerned with how a group of student teachers make sense of trigonometry. There are three main ideas in this study. This first idea is about the theoretical framework which focusses on the growth of mathematical thinking based on human perception, operation and reason. This framework evolves from the work of Piaget, Bruner, Skemp, Dienes, Van Hiele and others. Although the study focusses on trigonometry, the theory constructed is applicable to a wide range of mathematics topics. The second idea is about three distinct contexts of trigonometry namely triangle trigonometry, circle trigonometry and analytic trigonometry. Triangle trigonometry is based on right angled triangles with positive sides and angles bigger than 0 [degrees] and less than 90 [degrees]. Circle trigonometry involves dynamic angles of any size and sign with trigonometric ratios involving signed numbers and the properties of trigonometric functions represented as graphs. Analytic trigonometry involves trigonometric functions expressed as power series and the use of complex numbers to relate exponential and trigonometric functions. The third idea is about supportive and problematic conceptions in making sense of mathematics. This idea evolves from the idea of met‐before as proposed in Tall (2004). In this case, the concept of ‘met‐before’ is given a working definition as ‘a trace that it leaves in the mind that affects our current thinking’. Supportive conception supports generalization in a new contexts whereas problematic conception impedes generalization. Furthermore, a supportive conception might contain problematic aspects in it and a problematic conception might contain supportive aspects in it. In general, supportive conceptions will give the learner a sense of confidence whereas problematic conceptions will give the learner of sense of anxiety. Supportive conceptions may occur in different ways. Some learners might know how to perform an algorithm without a grasp of how it can be related to different mathematical concepts and the underlying reasons for using such an algorithm.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:589828 |
| Date | January 2013 |
| Creators | Chin, Kin Eng |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/58403/ |
Page generated in 0.0021 seconds